This invention pertains to a vibrating tube densimeter for measuring the density of fluids, either batchwise or continuously.
The principle of the vibration densimeter lies in the observation that the square of the vibration period at resonant frequency, sometimes called the natural vibration period, is a linear function of the mass of the vibrating body.
The density of the test fluid can be derived from first principles, knowing the volume of the tube, but it is generally more practical to calibrate the device empiracally using one or more fluids of known density.
Equation 1 relates the natural frequency (.omega.) of the vibrating tube to its mass. EQU .sup..omega. u.sup.2 =K.sub.f /m
wherein EQU .omega..sup.2 =.omega..sub.u.sup.2 -1/2(C/m).sup.2 ( 1)
wherein K.sub.f is the force constant and m is the mass of the tube and contents, .omega..sub.u is the undamped natural frequency of the system. C is the damping constant for the system and C/m is .omega..sub.u /Q where Q is proportional to the sharpness of the resonance frequency. In the ideal case, where Q is large, the resonance frequency is essentially .omega..sub.u.
The difference in density between a test fluid and a reference fluid in the vibrating tube is related to the difference in mass of the system in these two cases, since the interior volume (v.sub.I) of the tube is contant. Thus, one obtains ##EQU1## where the zero subscript refers to the reference fluid. In terms of the period of oscillation (.tau.), EQU (d-d.sub.o)=K(.tau..sup.2 -.tau..sub.o.sup.2) (3)
wherein K=K.sub.f /4 .pi..sup.2 v.sub.I. The calibration constant K can be determined from period measurements on two fluids of known density.
Art densimeters employing vibrating tubes employ a variety of means for vibrating the tube and sensing the induced vibration. Electrical means, which appear to be the more popular means, generally require the presence of electrical components such as insulated multi-turn electromagnetic coils or Piezo electric crystals adjacent to or on the tube. This has had the effect not only of complicating the devices but also limiting the conditions, especially temperature, under which they can be operated. For example, the devices of Kratky et al and Picker et al as described in Z. Angew, Phys. 27, 273 (1969) and in J. Solution Chem. 3 (5), 377 (1974) respectively, are limited, it appears, to operating temperatures below about 150.degree. C.
Patentees have contributed many devices. Representative of these are, for example, Janssen who in U.S. Pat. No. 3,728,893 teaches torsional oscillation of a U-tube with electrical sensing; Kratky et al who in U.S. Pat. No. 4,170,128 teach a device comprising a U-shaped bending type oscillator connected with a tensioned body responsive to temperature and pressure; Brockhaus who in U.S. Pat. No. 3,456,491 teaches a device comprising a straight pipe in a variable magnetic field adapted to oscillate at resonant frequency; Agar who in U.S. Pat. No. 3,763,692 teaches a process for measuring the absolute density of a fluid using a pipe for the fluid and a bar of the same material as a standard; Abbotts who in U.S. Pat. Nos. 3,623,357 and 3,648,512 teaches densimeters for gases which oscillate a hollow cylinder in a bell-like manner; Catherall who in U.S. Pat. No. 3,955,401 teaches a densimeter tube and cantilevers vibrating in antiphase; Kratky et al who in U.S. Pat. No. 3,910,101 teaches a device comprising mechanical to electrical transducer, influenced by an oscillatory mass containing the test fluid, connected to an electrical to mechanical, transducer acting on the mass; Supanick who in U.S. Pat. No. 4,170,894 teaches a four-step method comprising measuring the pulse repetition frequency of an oscillator containing air or a test gas; Ghahramani who in U.S. Pat. No. 4,215,566 teaches a Piezo crystal for sensing frequency and Muramoto who in U.S. Pat. No. 4,132,110 teaches a Piezo crystal to excite oscillation or vibration.
It is apparent that there is a need for, and it is an object of this invention to provide, a simple vibrating tube type densimeter capable of operation under severe conditions such as elevated temperature.